64.22.3 problem 1 (c)

Internal problem ID [13597]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 11, The nth order homogeneous linear differential equation. Section 11.8, Exercises page 583
Problem number : 1 (c)
Date solved : Monday, March 31, 2025 at 08:02:13 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

ode:=t^2*diff(diff(x(t),t),t)+(2*t^3+7*t)*diff(x(t),t)+(8*t^2+8)*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = \frac {c_2 \,{\mathrm e}^{-t^{2}}+c_1}{t^{4}} \]

✓ Mathematica. Time used: 0.071 (sec). Leaf size: 26

ode=t^2*D[x[t],{t,2}]+(2*t^3+7*t)*D[x[t],t]+(8*t^2+8)*x[t]==0; 
ic={}; 
DSolve[{ode,ic},{x[t]},t,IncludeSingularSolutions->True]
 

\[ x(t)\to \frac {2 c_1 e^{-t^2}+c_2}{2 t^4} \]

✓ Sympy. Time used: 0.828 (sec). Leaf size: 32

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(t**2*Derivative(x(t), (t, 2)) + (8*t**2 + 8)*x(t) + (2*t**3 + 7*t)*Derivative(x(t), t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \frac {C_{2} \left (- \frac {t^{6}}{24} + \frac {t^{4}}{6} - \frac {t^{2}}{2} + 1\right )}{t^{2}} + \frac {C_{1}}{t^{4}} + O\left (t^{6}\right ) \]